# Circles Can be Cool Too!

Geometry Level 4

Circle $$\omega _ {1}$$ with center $$A$$ and circle $$\omega _{2}$$ with center $$B$$ have radii $$7$$ and $$2$$ respectively. The two circles intersect at points $$T$$ and $$Y$$ such that $$TY = 2$$. Let $$P$$ be a point outside of both circles such that $$PA = 9$$ and $$PB = 6$$. The area of $$\bigtriangleup PAB$$ can be expressed as $$\frac{a\sqrt{b}}{c}$$ such that $$b$$ is a square-free integer and $$a$$ and $$c$$ are relatively prime integers. Find $$a+b+c$$.

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